Precession & Proper Motion: JNow

[OzDave]

Hi,

Suppose I have coordinates for a star published in a catalog using equinox B1950 (or J2000 or whatever) and I want to calculate the coordinates of the star today. How should I go about this?

Googling around a bit, I found two things. Firstly, I have to take into account the Proper Motion of the star between the catalog year and now. So this means applying the RA and DEC motion updates to the catalog coordinates.

Once I've done that, I should have accounted for how far the star moved on its own. Next I have to account for the precession of the earth during the time period in question. I am sure I can find a calculation for doing that, but basically this shifts the coordinates of all stars to account for the change in direction of the Earth's polar axis.

So if I perform these two steps, will the resulting coordinates represent JNow for the star, or did I miss a step, or misunderstand something?

Any guidance much appreciated. I can do the math, just need to understand if I'm on the right track with it.

Regards,

David

[Demonperformer]

Next I have to account for the precession of the earth during the time period in question. I am sure I can find a calculation for doing that

There is a table in Norton for doing this bit [in my 19th edition it is on page 42]

[FraserClarke]

Yep, think you're on the right track.

Do you have the equations already? There are also a few on-line coordinate convertors as well, though I'm not sure they deal with proper motion.

[OzDave]

I've seen some online converters, but basically I am coding some stuff for pointing a telescope and I want to get my coordinates from a catalog and have them updated for NOW so the scope will point accurately.

I've also seen various code on the web for doing the conversion, mostly involving going from B1950.0 to J2000.0. However, I wanted something a bit more general.

I found a technique that works by converting the RA/DEC coordinates to cartesian XYZ coords, where the Z axis is aligned with the celestial pole, the X axis points at the vernal equinox (First point of Aries as it seems to get called), and Y is orthogonal to X and Z.

You then multiply the XYZ coords by a Precession Matrix which seems to be hardcoded into all the programs I've seen with a pile of magic numbers and caveats like don't use it for points near the poles, or it only works for B1950 to J2000.

The matrix multiply is supposed to twirl the XYZ axes about a bit to model the precession of the earth. The result is your precessed coordinate, but still in XYZ, so you have to convert back to RA/DEC.

My problem is how to compute a general purpose precession matrix. If I understood that bit, I think I'd probably have a solution. Anyone have an idea how to compute that kind of thing? I understand matrix multiplies and affine transformations as that is relatively common in 3D computer graphics, I'm just not sure what combinations of rotations I'd need to model a given precession from one epoch/equinox to NOW.

Hope someone can help, otherwise I'll keep Googling.

David

[FraserClarke]

If you're writing a TCS, get yourself a copy of SLALIB from Pat Wallace. This is the heart of almost all TCS's and is very fully featured and very well debugged. I think if you're doing this non-commerically, he'll give you the library for free.

Tpoint Software Products and Services

[Demonperformer]

Maybe I'm being stupid, but when you align the mount, won't it still be assuming that the alignment stars you have selected are in J2000 (or whatever) position? And if you can never point the telescope more accurately than it is aligned ...

Don't want to 'wet blanket' your project, but I can't see that it is going to result in more accurate pointing, with the possible exception of stars that have really high proper motions ...

[OzDave]

DP, the software I am doing will take care of the alignment process. That is why I want to precess the coordinates. The software controls the mount entirely, so it will only be assuming what my software tells it.

David

[OzDave]

If anyone is interested, I ended up finding this link to an excellent reference on the subject:

Fundamental astronomy - Google Books

David

[themos]

This forum is excellent! Thanks, I was looking for this and Google was no help at all...

[OzDave]

Are you looking for source code to compute the precession stuff?

I translated the maths I found online into some useful functions if you are interested. They are in C.

David

[themos]

Thanks but I've done it now already.